Slowdown Services: Staffing Service Systems with Load-Dependent Service Rate

Operations Research, vol. 63, No. 2, pp. 305-324, 2013

39 Pages Posted: 29 Aug 2013 Last revised: 29 Aug 2018

See all articles by Jing Dong

Jing Dong

Columbia University

Pnina Feldman

Questrom School of Business, Boston University

Galit Yom-Tov

Technion-Israel Institute of Technology

Date Written: August 28, 2013

Abstract

Many service systems exhibit service slowdowns when the system is congested. Our goal in this paper is to investigate this phenomenon and its e ffect on service performance. We modify the Erlang-A model to account for service slowdowns and perform an asymptotic analysis in the Quality-and-Efficiency Driven (QED) regime. We find that when the load sensitivity is low, the system can achieve QED performance, but the square root staffing parameter requires an adjustment to achieve the same performance as an ordinary Erlang-A queue. When the load sensitivity is high, the system alternates randomly between a QED and an Efficiency Driven regime performance levels. To stabilize and improve system performance in this case, we propose two solutions: to add staffing on a permanent basis or to implement a threshold admission control policy where customers are occasionally blocked or rerouted to other service systems. The former is a static solution that provides a Quality Driven regime performance, while the latter is a real-time dynamic solution that leads to QED performance.

Keywords: Service systems, Halfin-Whitt regime, QED, Erlang-A model, State dependent queues, Load dependent queues, Bi-stability

Suggested Citation

Dong, Jing and Feldman, Pnina and Yom-Tov, Galit, Slowdown Services: Staffing Service Systems with Load-Dependent Service Rate (August 28, 2013). Operations Research, vol. 63, No. 2, pp. 305-324, 2013, Available at SSRN: https://ssrn.com/abstract=2317410 or http://dx.doi.org/10.2139/ssrn.2317410

Jing Dong

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Pnina Feldman (Contact Author)

Questrom School of Business, Boston University ( email )

Boston, MA
United States

HOME PAGE: http://https://www.bu.edu/questrom/faculty-research/faculty-directory/pnina-feldman/

Galit Yom-Tov

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

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